From C = T + M to C = T + R: Preparing an Event-First Causal Budget Framework

From C = T + M to C = T + R: Preparing an Event-First Causal Budget Framework

This document is a transition piece in the Causal Budget Framework (CBF) series. It clarifies three interpretive points that prepare for a shift in emphasis toward an event-first formulation.

1. Clarifies the role of the Lorentz factor. The original CBF work presented the budget constraint C = T + M in a way that could suggest the Lorentz factor emerges from budget arithmetic. This document corrects the conceptual ordering: the Lorentz factor arises from frame synchronization and constrains how the budget partitions, not the other way around.

2. Renames the budget terms. Translation (T) becomes Transport, the capacity to carry unresolved causal structure forward. Maintenance (M) becomes Resolution (R), the total capacity to commit events. These renames reflect a shift in emphasis from particle persistence to event commitment, without changing the underlying dynamics.

3. Clarifies that mass lives inside Resolution. R contains two components: Resting M (the portion consumed by identity self-commitment, the ongoing work of remaining the same particle) and available interaction capacity. Heavy particles consume most of R maintaining identity; light particles consume less; photons consume none. Mass is the cost of self-continuity.

Relation to prior work:

Parts I–III explored CBF through cellular automata, wave propagation, and budget partitioning. Those results remain valid. This document reframes their conceptual foundation and signals a forthcoming event-first treatment where spacetime and relativistic effects emerge from event resolution and frame synchronization.

Keywords: Causal Budget Framework, event-first physics, frame synchronization, Lorentz factor, resolution, transport, computational physics